Srednicki equation 5.10

In equation 5.10, second line srednicki uses the same definition as eq 5.6, while 5.6 is time independent [tex]a_1^{\dagger}(k)[/tex] and in 5.10 we have to use the new time dependent [tex]a_1^{\dagger}(t)[/tex] . Why dont we have a new [tex]a_1^{\dagger}(t)[/tex], which say explicitly depends on t ?